A125523 Democratic primes: primes such that the left half of the prime is prime and the right half is not.

29, 31, 59, 71, 79, 211, 229, 239, 241, 251, 269, 271, 281, 311, 331, 349, 359, 379, 389, 509, 521, 541, 569, 571, 599, 701, 709, 719, 739, 751, 761, 769, 1109, 1151, 1163, 1181, 1187, 1193, 1301, 1321, 1327, 1381, 1399, 1709, 1721, 1733, 1777, 1787, 1901

Offset: 2

Author

Cino Hilliard, Jan 22 2007

Keywords

• base
• easy
• nonn

Comments

If the length of n is odd then the central number is not used in the calculation. So neither the left half nor the right half will contain the central digit. If the length of n is even, then all numbers are used.

Examples

			The left half of 29 is 2, which is prime. The right half is 9, which is not prime.
The left half of 211 is 2, which is prime. The right half is 1, which is not prime.
		

Links

• Tony Padilla and Brady Haran, The Most Evil Number, Numberphile video (2018)

Crossrefs

Cf. A125524, A125525.

Programs

PARI

/* Political primes, democratic case. */ dem(n) = { local(x,ln,y,lp,rp); forprime(x=2,n, y=Str(x); if(x > 9, ln=floor(length(y)/2), ln=1); lp = eval(left(y,ln)); rp = eval(right(y,ln)); if(isprime(lp)&& !isprime(rp),print1(x",") ) ) }